Questions tagged [kerr-metric]

The Kerr metric describes the geometry of empty spacetime around a rotating uncharged axially-symmetric black hole.

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Wouldn't Miller's planet be fried by blueshifted radiation?

In Interstellar, wouldn't Miller's planet be fried by blueshifted radiation? The 61,000x time dilation multiplier would make even cosmic background radiation photons into extreme UV photons. I was ...
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Delta-v for orbital changes around a Kerr black hole

What's the Delta-v to change between the Marginally bound orbit and the innermost stable circular orbit around a Kerr black hole.
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Temperature of a rotating/charged black hole

How do you calculate the temperature of a rotating or charged black hole? How will rotation/charge affect the lifetime?
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General Relativity, Space-time geometry around a rotating body is described by the Kerr line element [closed]

Could you please help with some equations in the homework of General relativity? Here I attach the image of some equations to be derived or proved. I would be very grateful just to understand how to ...
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Is there an equation for retrograde equatorial orbital radii around a Kerr black hole as compared to a Schwarzschild black hole?

A non-rotating, non-charged, Schwarzschild black hole has an event horizon with radius $r_s = \frac{2 G M} {c^2}$, where $M$ is the mass of the black hole, $G$ is the gravitational constant, and $c$ ...
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Current status and reference request for the Black Hole Stability Conjecture

The Black Hole Stability Conjecture is one of the most important open problems in the field of General Relativity, and remains open in spite of the advances in the past half century. To test Einstein’...
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Kerr Solution metric ansatz for EFEs

The Schwarzschild metric ansatz is given by $$ds^2=-A(r)dt^2+B(r)dr^2+r^2d \Omega^2$$ where upon applying the Einstein Field Equations $$G_{\mu\nu}=\kappa T_{\mu\nu}$$ we obtain the normal ...
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Interpretation of Angular Momentum flux from stress energy tensor in Black hole superradiance

While studying the superradiance of a scalar field in Kerr geometry, we show that the energy and angular momentum of the Kerr black hole are extracted by the superradiant modes. I understand the ...
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What spins as a black hole? (lame question) [duplicate]

Obviously I am not a physicist. I have seen What is black hole spin? but this is not what puzzles me. If I understand correctly, black hole has only three features (please correct me): angular ...
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Conformally flat slices in Kerr spacetime

I heard some references to ''conformal Kerr'' in general relativity and I'm not sure what this means. It presumably cannot be referring to a conformally flat slice of Kerr spacetime, since the Kerr ...
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Penrose process and the change in irreducible mass

This is a minor confusion. In various lectures notes, for example by Carrol or by Strominger, when discussing the Penrose process of extracting energy from the Kerr black hole, they will exploit the ...
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Condition on particle momentum crossing the Kerr horizon

Around the equation (7.143) in [Carroll] Lecture Notes on General Relativity, the note talks about momentum $p$ of a particle entering the ergosphere and crossing the outer horizon. The claim is that ...
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Derivatives of GHP scalars for typeD spacetimes

Are there any algebraic expressions for $\eth \overline \rho$ and $þ (\overline{\tau}')$ in the GHP formalism? In the specific case of the Kerr metric, by explicit calculation, I managed to prove that ...
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Finding event horizon and ergosphere

I am trying to calculate the event horizon and ergosphere of the Kerr metric. However, I could not seem to find a proper derivation or formula to calculate the event horizon and ergosphere. Could ...
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Outer horizon in the Kerr metric

I have a question about the horizon of a Kerr black hole. Assuming that the metric has a coordinate singularity for $\Delta=0$, namely when $$r_\pm=GM\pm\sqrt{G^2M^2-a^2}$$ how can the outer horizon ...
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What is missing to make this depiction of a Black Hole realistic?

So i am working on a Music video as a FX Artist and part of the job is a Black Hole. Now i am fairly confident that i am just about the only one on the team who cares how accurat the party is. But i ...
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Finding the transformation for the Newman-Penrose formalism

I am working with the Kerr metric (suppose it is $g_{\mu \nu}$) where I want to understand how the Teukolsky master equation is derived using the Newman-Penrose formalism. The original article can be ...
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What does it mean that the inner event horizon of a kerr blackhole is unstable? [duplicate]

I have read that the inner horizon of a Kerr black hole is unstable? What does this mean and what would the inner event horizon become?
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Possible erratum in Hartle's book "Gravity" in example 15.1

I'm reading Hartle's book Gravity (2014), and I think there's an erratum in example 15.1. In this example, he says that for a massive particle at infinity at rest, which starts falling radially ...
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Where is the CTC region of a Kerr Black Hole?

CTCs are found in the region where $r < 0$ . That should be just inside the ring singularity, since in Boyer Lindquist coordinate system $r = 0$ means ring singularity. Does that mean this image ...
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Kerr metric geodesics using EL equations

Let there exist a Kerr metric $ds^2$ in Boyer–Lindquist coordinates such that $$ds^2=-\left(1-\frac{r_sr}{\Sigma}\right)dt^2+\left(\frac{\Sigma}{\Delta}\right)dr^2+\Sigma d \theta^2+\left(r^2+a^2+\...
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A little more detail on the definition of Angular Moment parameter for a Kerr Black Hole

In several places, such as Explain Kerr-Newmann Black Hole Spins in SI Units, the parameter $a$ is defined as: $$a = \frac{Jc}{GM^2}$$ My question is whether the angular momentum J can be defined in ...
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Is accretion disc caused by frame dragging?

Is accretion disc around a Kerr black hole the result of its frame dragging?
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Why is Kerr Singularity ring shaped?

Why is the Kerr singularity like a ring — not a 3-D ellipsoid, or a point, or even a flattened disk? I need an intuitive answer, please.
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Equivalence Principle Frame Dragging

Why do metric equations of a rotating body (like Kerr Metric for black holes or EFE solution for rotating bodies) contain a dt dphi term, leading to rotational frame dragging effects? Please don't ...
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Why is Kerr Spacetime unstable?

How do we know from the Kerr Metric that it is unstable near the Cauchy Horizon? What causes this unstability?
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Crossing a Kerr wormhole

You cannot cross an Einstein Rosen Bridge because it needs faster than light speed to cross it. But the same is not true for a Kerr wormhole, it lies beyond the Cauchy Horizon and you do not need FTL ...
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Watching Kerr Ring Singularity

Can you see light from ring singularity from inside the Cauchy Horizon? In between 2 horizons space and time coordinate swaps places, so the inside region lies at the future. But after crossing Cauchy ...
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Negative $r$ in Boyer-Lindquist system

I am confused about the Boyer Lindquist System. $r = 0$ at the ringularity, and outside that $r$ should be positive (intuitively). But this paper on closed CTCs in Kerr Spacetime claims that $r < 0$...
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Ιn a Kerr Spacetime (for example) how can you relate the simultaneity of a ZAMO observer with the coordinate time $t$?

So bear with me if you can. I will try to type my understanding (which is bad) to this subject (regarding simultaneity), what's exactly the question and why it has came up. Why Reading some papers on ...
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If a very massive object enters in a rotating black hole retrograde orbit should it slow down the black hole's spin?

If a very massive object is orbiting retrograde around a rotating black hole, would it slow down the black hole's spin? Of course, due to its interaction with the black hole's rotating frame, better ...
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Is the spin of a black hole affected by the matter orbiting it?

It's well understood that the moon has an effect on how much the earth spins. My understanding is that if the moon was bigger, it could impact tidal forces to a larger extent, and possibly slow the ...
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What do you see as you look outwards while falling into a Kerr black hole?

Take the Kerr black hole and consider an infalling observer, say equatorial and with zero initial angular momentum for the sake of simplicity. Using the standard metric in Boyer Lindquist coordinates ...
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What happens to the ergospheres of two colliding black holes, right before collision?

Let's assume we have two black holes with equal mass. They move towards each other, each heading towards the center of the other black hole. Both black holes rotate with equal speed. What happens to a ...
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Does the twist of spacetime by a black hole increase over time?

From the Wikipedia page about Ergospheres: As a black hole rotates, it twists spacetime in the direction of the rotation... Does this "twisting up spacetime" add up over time in any ...
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How to plot the cross section of event horizon of hairy kerr black hole?

I was growing through the paper "Parameter estimation of hairy Kerr black holes from its shadow and constraints from M87*" whose link is https://arxiv.org/abs/2103.11417. In the paper it ...
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Mass change of a black hole during the Penrose process

I have been reading about Kerr black holes, specifically via Hobson et. al, General Relativity: An Introduction for Physicists. When discussing the Penrose process, the book considers a particle A ...
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Black holes in general relativity: angular velocity of the horizon

I was studying Killing horizons in General Relativity and I met some difficulties on the following point. In a stationary, axisymmetric and asymptotically flat black hole, we know that there exist two ...
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Can the curvature of space-time be also described as a 'frame' (space) whirlpool?

Can the curvature of space-time be also described as a 'frame' (space) wirlpool? When we talk about the Schwarzschild metric it can be immagined as a curved manifold but in the Kerr metric it seams ...
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Rotating Observers in Kerr Spacetime

I am learning about the Kerr metric and I am using the book Gravitation - Foundations and Frontiers by T. Padmanabhan. While discussing a 'static limit' he considers an observer rotating with an ...
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Killing Horizons in the Kerr Metric

I seem to be quite confused with Killing vector fields, Killing horizons and null horizons, especially in the context of the Kerr metric. I have a couple of questions regarding this, and the text I am ...
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Singularities of the Coordinate Systems

We know that, the singularity of the Schwarzschild metric at $r=2M$ can be removable via coordinate transformation to Kruskal-Szekers . Can we apply a similar argument to the Kerr metric? If so, what'...
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Orbital Photon Speed at the equatorial plane of a rotating black hole

I've been trying to calculate $d\phi/dt$ of photons orbiting a Kerr black hole (Kerr metric in Boyer-Lindquist coordinates) on the equatorial plane, both counter and along with its rotation. So I used ...
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Event horizon of a rotating black hole

For a non-rotating black hole, Schwarzschild radius itself forms the event horizon, but how do we find the event horizon of a rotating Kerr black hole?
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What is the relative importance of the Coriolis term to the precession term in frame dragging by rotating Kerr black holes?

The Wikipedia entry for Thirring precession describes the Coriolis term as separate from the precession term. Is it fair to say that when looking at the dynamics of a rotating black hole, the ...
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Light scattering on the rotating black hole in the Kerr geometry

To simulate light scattering on the rotating black hole we have used this paper and this code. First, we made animation for light beam scattering in the equatorial plane For not equatorial plane the ...
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Where is the black hole horizon in ingoing Kerr coordinates?

In ingoing Kerr coordinates, the metric of the Kerr black hole spacetime is: \begin{equation} ds^2 = -\left(1-\frac{2Mr}{\Sigma}\right)dv^2 +\frac{2Mr}{\Sigma}\left(dr-a \mathrm{sin}^2\theta d\phi\...
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Undefined symbol in Catalogue of Spacetimes (Kerr metric)

In the Catalogue of Spacetimes, in the Kerr metric section, under "General local tetrad", there is a cluster of four equations (strangely labeled 2.14.6a and 2.14.6b!), two of which contain ...
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Exceeding the Kerr black hole spin limit

It is well known that the limit on the angular momentum for a Kerr black hole is given by \begin{equation} 0 \leq a^* \leq 1 \quad \text{where} \quad a^* \equiv \frac{cJ}{GM^2} \end{equation} and $J$ ...
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Kerr metric in Eddington–Finkelstein form

I am searching for a reference in which I can find out the Kerr metric in Eddington–Finkelstein form. I have computed it by hand and I have obtained the following form but I am not sure above all of ...
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